Encyclopedia of Humor

Theorem: n=n+1

Proof:
(n+1)^2 = n^2 + 2*n + 1

Bring 2n+1 to the left:
(n+1)^2 – (2n+1) = n^2

Substract n(2n+1) from both sides and factoring, we have:
(n+1)^2 – (n+1)(2n+1) = n^2 – n(2n+1)

Adding 1/4(2n+1)^2 to both sides yields:
(n+1)^2 – (n+1)(2n+1) + 1/4(2n+1)^2 = n^2 – n(2n+1) + 1/4(2n+1)^2

This may be written:
[ (n+1) - 1/2(2n+1) ]^2 = [ n - 1/2(2n+1) ]^2

Taking the square roots of both sides:
(n+1) – 1/2(2n+1) = n – 1/2(2n+1)

Add 1/2(2n+1) to both sides:
n+1 = n

Theorem: 1 + 1 = 2
Proof:
n(2n – 2) = n(2n – 2)
n(2n – 2) – n(2n – 2) = 0
(n – n)(2n – 2) = 0
2n(n – n) – 2(n – n) = 0
2n – 2 = 0
2n = 2
n + n = 2
or setting n = 1
1 + 1 = 2

Theorem: 3=4
Proof:

Suppose:
a + b = c

This can also be written as:
4a – 3a + 4b – 3b = 4c – 3c

After reorganizing:
4a + 4b – 4c = 3a + 3b – 3c

Take the constants out of the brackets:
4 * (a+b-c) = 3 * (a+b-c)

Remove the same term left and right:
4 = 3

Theorem: All positive integers are equal.

Proof: Sufficient to show that for any two positive integers, A and B, A = B.

Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B.

Proceed by induction.

If N = 1, then A and B, being positive integers, must both be 1. So A = B.

Assume that the theorem is true for some value k. Take A and B with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence (A-1) = (B-1). Consequently, A = B.

President Clinton, speaking in private with his advisor on public favor, told him that the planned invasion of Haiti will be the most unpopular thing that he has ever done as the President of the United States.

“Actually, sir, according to our research, the most unpopular thing you’ve ever done was to be inaugurated as President. It’s just been downhill from there.”